{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:DM3HETNZDOSPZ5M2ZU2EDKRXNS","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"7dcbe84df318c5375837b2873bc48d0d17245ee03f49caddce37a9079f03943d","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2009-10-12T12:29:15Z","title_canon_sha256":"0fe24454d044515aef7e63cbe5cdff82acaefb2a7b76d31d70fd3a2ed406af9f"},"schema_version":"1.0","source":{"id":"0910.2147","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0910.2147","created_at":"2026-05-18T04:25:37Z"},{"alias_kind":"arxiv_version","alias_value":"0910.2147v1","created_at":"2026-05-18T04:25:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0910.2147","created_at":"2026-05-18T04:25:37Z"},{"alias_kind":"pith_short_12","alias_value":"DM3HETNZDOSP","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_16","alias_value":"DM3HETNZDOSPZ5M2","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_8","alias_value":"DM3HETNZ","created_at":"2026-05-18T12:25:59Z"}],"graph_snapshots":[{"event_id":"sha256:db7edb92aba298b1f1bdbb6317fafd2672fd281c9b8610842e978746eb446dcb","target":"graph","created_at":"2026-05-18T04:25:37Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We study the semidirect product of a Lie algebra with a representation up to homotopy and provide various examples coming from Courant algebroids, string Lie 2-algebras, and omni-Lie algebroids. In the end, we study the semidirect product of a Lie group with a representation up to homotopy and use it to give an integration of a certain string Lie 2-algebra.","authors_text":"Chenchang Zhu, Yunhe Sheng","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2009-10-12T12:29:15Z","title":"Semidirect products of representations up to homotopy"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0910.2147","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:dd6fb326bf9a25b859509a4a6cd21829365f768c82f8853cfbfc8ad180f52134","target":"record","created_at":"2026-05-18T04:25:37Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"7dcbe84df318c5375837b2873bc48d0d17245ee03f49caddce37a9079f03943d","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2009-10-12T12:29:15Z","title_canon_sha256":"0fe24454d044515aef7e63cbe5cdff82acaefb2a7b76d31d70fd3a2ed406af9f"},"schema_version":"1.0","source":{"id":"0910.2147","kind":"arxiv","version":1}},"canonical_sha256":"1b36724db91ba4fcf59acd3441aa376cb255e117942f3997e6db65e49edd218d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1b36724db91ba4fcf59acd3441aa376cb255e117942f3997e6db65e49edd218d","first_computed_at":"2026-05-18T04:25:37.940364Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:25:37.940364Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0Wj9OkTsMNgwQP2sZbzlRH2HAGblAanou4YlwCN6HMnALubfCe5Yy1VM9X6UNAwq8V9BDk9/nBrGiaWjNpedDg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:25:37.940793Z","signed_message":"canonical_sha256_bytes"},"source_id":"0910.2147","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dd6fb326bf9a25b859509a4a6cd21829365f768c82f8853cfbfc8ad180f52134","sha256:db7edb92aba298b1f1bdbb6317fafd2672fd281c9b8610842e978746eb446dcb"],"state_sha256":"406557b353f5c670de75e3c54143de279d8934b6c6a7d65b4c470fd2cc24e89b"}